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Gas Storage Valuation Methodologies, Quantitative Analysis & Trading Strategies

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Gas Storage Valuation Methodologies, Quantitative Analysis & Trading Strategies Storage Valuation Gas Storage Valuation Methodologies, Quantitative Analysis & Trading Strategies Presented to the International Centre for Mathematical Sciences in Edinburgh by : Dario Pavlos Ghazi Tuesday 29 th January 2009 • To obtain the presentation: • Email: [email protected] • Subject: ICMS Presentation Dario Ghazi Int tel: 252534 Quantitative Analyst Ext tel: +44 (0)1753 492534 Centrica Energy Mob: +44 (0)7789 573957 Fax: +44 (0)1753 431150 Millstream East Maidenhead Road Windsor Berkshire SL4 5GD www.centrica.com Presentation Summary • Key gas storage functions. • Comparison of different valuation quantitative techniques. • Quantitative analysis of the valuation steps. • Measuring the extrinsic value risk. • Storage trading strategies. • Key gas storage functions. • Comparison of different valuation quantitative techniques. • Quantitative analysis of the valuation steps. • Measuring the extrinsic value risk. • Storage trading strategies. Key gas storage functions Why storage facilities are developed? • Three key functions behind the development of storage facilities: • Seasonal cycling – Shifting the summer gas production capacity into winter. • Peaking service/peaking deliverability – Responding fast to changing conditions and controlling the peak demand, i.e in cold days. (The advantage of a fast turning storage facility). • Balancing service – Balancing unpredicted small variations in demand/supply. Maintaining quick deliverability when pipeline system has been disrupted. • Key gas storage functions. • Review of different valuation quantitative techniques. • Quantitative analysis of the valuation steps. • Measuring the extrinsic value risk. • Storage trading strategies. Review of different valuation quantitative techniques Hedging with storage using the forward curve Purchases The Q1-Summer spread provides a good hedge in forward markets. D J F M A M J J A S O N Once market monthly contracts trade one can optimise position to fit optimal profile Initial Hedge Shape to give Q1-Summer p/th Sales Optimal hedge Shape to give 1.057 x (Q1-Summer) p/th Review of different valuation quantitative techniques How easy is it to get the storage value? • Storage valuation function does not have a closed-form solution, therefore, alternative approaches are suggested. • Storage is probably the most complicated option structure in energy markets. Its complexities exceed even those of power generation. • Storage Value = Withdrawal Revenue – Injection Cost. • However, given the option characteristics that storage gives and the forward curve variability, we need to estimate the solution using simulations for price paths and storage optimal volume spreads. Review of different valuation quantitative techniques Storage Valuation Approaches • Three main valuation approaches: • Forward optimisation, • Forward dynamic optimisation, • Combinations. Review of different valuation quantitative techniques Forward Optimisation Approach • Forward optimisation approach: i , j FV ( F t ; S , I , W , t ) = ∑ ∆ F t V i , j (F t ; S , I , W , t ) i < j Where : FV = Forward Value F t = Forward Price V i , j = Optimal Spread Volumes S = Space I = Injection W = Withdrawal • Value is s.t physical constraints (S, I, W). • Storage value is the summation of all optimal spread volumes multiplied by the corresponding forward prices. • Optimal spread volumes are the net volumes for a given period (i.e a month) spread. Negative spreads are not considered (=0). Review of different valuation quantitative techniques Forward Optimisation Approach continued • Decision volume variable V is a function of the forward contracts prices at injection and it can be defined as: • The net volumes for a given period (i.e a month) and assuming as an optimal strategy to turn the storage facility’s inventory only once or more, • The net volumes for a given spread period (i.e monthly). • The advantages of using as a decision variable the volumes for a given spread is that this procedure suggests a hedging strategy, i.e long in summer and short in winter. • This hedging strategy is static and is only revised to discount the cash flows. The cash flows will not change regardless of the future evolution of the forward curve. Review of different valuation quantitative techniques Forward Dynamic Optimisation Approach • Forward Dynamic Optimisation Approach: • This approach takes into account that re-adjustment of the optimal hedges every time the forward curve moves to our favour this will result in a greater storage value without the downside risk. • This strategy is a spread option position. T Spread Option Value = FV (Ft ; S , I ,W ,t0 ) + Et [ ∑ max( FV i − FV i−1 ), ]0 0 0 i=t0 +1 • The storage value is a portfolio of complex spread options. • The value of the spread option is a function of the value of the forward contracts plus the risk-neutral expectation of the future forward value spread. Review of different valuation quantitative techniques Forward Dynamic Optimisation Approach continued • The factor driving the spread option values (storage value) is the variability of the forward curve. • The variability of the forward curve is a function of each single forward contract’s volatility and their correlation structure. • The challenge is to hedge the time value (or else extrinsic value) of the option. Review of different valuation quantitative techniques Decomposing the storage value • Intrinsic Value = Valuation on the Forward Curve. • Rolling Intrinsic = Re-adjusting the Intrinsic value evolution every time the FC moves to our favour. • Extrinsic Value = Total Value – Intrinsic Value. • The three key drivers of the additional value (or time value or extrinsic) are: • The shape of the forward curve. The wider and more variable the summer-winter gap , the greater the additional value. • Volatility, mean reversion, correlation (between forward contracts). Higher volatility, lower MR, lower correlation, higher option time value. • Storage facility’s operational flexibility. Higher flexibility, higher both intrinsic and extrinsic values. Review of different valuation quantitative techniques Decomposing the storage value S10 S40 8.00 16.00 7.00 14.00 6.00 12.00 5.00 10.00 4.00 8.00 3.00 6.00 2.00 4.00 2.00 1.00 0.00 0.00 Intrinsic Rolling Intrinsic Extrinsic Total Value Intrinsic Rolling Intrinsic Extrinsic Total Value S75 • Intrinsic/Total Value Ratio: 18.00 16.00 Seasonal > Medium > Short Duration 14.00 12.00 10.00 8.00 • Extrinsic/Total Value Ratio: 6.00 4.00 Short Duration > Medium > Seasonal 2.00 0.00 Intrinsic Rolling Intrinsic Extrinsic Total Value Review of different valuation quantitative techniques Decomposing the storage value Storage Value Split by Service Duration 140.00 120.00 100.00 80.00 Extrinsic 60.00 Intrinsic 40.00 Value (p/th of space) of (p/th Value 20.00 - 10 20 30 40 50 60 70 80 90 100 Service Duration (Days) Review of different valuation quantitative techniques Intrinsic Value Analysis 20 18 16 14 12 10 8 6 4 2 0 S=10 S=40 S=75 Intrinsic (Q-M) Intrinsic (Q-S) Intrinsic (M) Intrinsic (F) • All four models give roughly the same intrinsic values, therefore, trading on the forward curve without any price variability will generate the same amount of profit regardless of the models or methodology we are using. Review of different valuation quantitative techniques Extrinsic Value Analysis 7 6 5 4 3 2 1 0 S=10 S=40 S=75 Extrinsic (Q-M) Extrinsic (Q-S) Extrinsic (M) Extrinsic (F) • The greater the model flexibility, the more flexible the extrinsic value. • Extrinsic value differs across models due to the different pricing algorithms for gas prices and the numerical methodology in order to solve the storage function optimisation problem. Review of different valuation quantitative techniques How important is extrinsic value? • According to industry experts, the time value (extrinsic) of storage can be from a fraction of the intrinsic (like ¼) up to seven or even eight times the intrinsic value. • The intrinsic and extrinsic values of storage are defined exactly as the intrinsic and extrinsic values of options, since storage is an option. Therefore, extrinsic value has the same properties as in finance: • It increases along with volatility and it declines as we approach maturity (T). The further out we stand, the greater the time -value of storage. • Being able to estimate this time value is to be able to figure out how to unlock extra value, beyond the intrinsic. • The most flexible pricing model is employed by model “M” (stochastic winter-summer spread), therefore, exhibits the most flexible extrinsic value. • Furthermore, some trading strategies are shown at the end on how to generate greater than intrinsic cash flows by using calendar spread options. Review of different valuation quantitative techniques Storage value sensitivity analysis • Storage value is sensitive to both market parameters and physical constraints. • Market parameters: • Volatility • Correlation • Mean reversion • Physical constraints: • Injection • Withdrawal • Total space Review of different valuation quantitative techniques Storage value sensitivity to volatility • Volatility has a positive impact on value. • Vega is one of the Greeks in financial mathematics, it shows the sensitivity of the storage option value to volatility: ∂V/∂σ • Value Sensitivity to Vol: Short duration > Medium duration > Seasonal Storage Vol Effect On Value Vega Surface 40.0 35.0 20.0 30.0 25.0 15.0 20.0 V a lu e % Change 15.0 10.0 10.0 5.0 5.0 S4 0.0 S3 200 220 240 260 280 300 320 340 360 380 400 dVol 0.0 S2 Vol S=10 S=40 S1 S=75 S=10 S=40 S=75 Storage Review of different valuation quantitative techniques Calendar Spread Option Value Sensitivity to Correlation CS Option Premium 0.07000000 0.06000000 0.05000000 0.04000000 0.03000000 0.02000000 European0.01000000 Call Price 0.00000000 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Futures Spread Correlation Review of different valuation quantitative techniques Storage value sensitivity to MR • Energy prices have shown to revert to a long-run level (marginal cost level).
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